Hardness of Online Sleeping Combinatorial Optimization Problems
Abstract
We show that several online combinatorial optimization problems that admit efficient no-regret algorithms become computationally hard in the sleeping setting where a subset of actions becomes unavailable in each round. Specifically, we show that the sleeping versions of these problems are at least as hard as PAC learning DNF expressions, a long standing open problem. We show hardness for the sleeping versions of Online Shortest Paths, Online Minimum Spanning Tree, Online k-Subsets, Online k-Truncated Permutations, Online Minimum Cut, and Online Bipartite Matching. The hardness result for the sleeping version of the Online Shortest Paths problem resolves an open problem presented at COLT 2015 [Koolen et al., 2015].
Cite
Text
Kale et al. "Hardness of Online Sleeping Combinatorial Optimization Problems." Neural Information Processing Systems, 2016.Markdown
[Kale et al. "Hardness of Online Sleeping Combinatorial Optimization Problems." Neural Information Processing Systems, 2016.](https://mlanthology.org/neurips/2016/kale2016neurips-hardness/)BibTeX
@inproceedings{kale2016neurips-hardness,
title = {{Hardness of Online Sleeping Combinatorial Optimization Problems}},
author = {Kale, Satyen and Lee, Chansoo and Pal, David},
booktitle = {Neural Information Processing Systems},
year = {2016},
pages = {2181-2189},
url = {https://mlanthology.org/neurips/2016/kale2016neurips-hardness/}
}